In my theses, I need to include a section on computational complexity

of the Simplify function.  I am simplifying addition of rational functions like this:

VAR0 := -(t^2+2*t+1)/(t-1)/(1-2*t+t^2);
VAR1 := (t^3+1)/(-1+t)/(-1+t^3);
VAR2 := (t^2+1)/(-1+t)/(-1+t^2);
VAR3 := (t^3+1)/(-1+t)/(-1+t^3);
MyResult:=VAR0 + VAR1 + VAR2 + VAR3;
MyResult:=simplify(MyResult);

I would like to get help with the comlexity question and/or what algorithm(s)

are used in this type of simplification.